Number System in Digital Electronics

Hi,

Friends I forgot about the number system it's the basic thing in Digital Electronics. There are two types of numbering system:

1. Non-positional
2. Positional 

The most widely used number system is a positional number system. This number system has a 'radix' or 'base'. The weight of a digit depends on its relative position, within the number.

For example:
In our school days i.e. in lower classes we do these kinds of sums
2815.228 is taken as an example

Now, Dividing the above number into the following

    2×10＾3  +  8×10＾2  +  1×10＾1  +  5×10＾0  +  2×10＾-1   +  2×10＾-2   +  8×10＾-3
       1000             100             10                 Unit             1/10                1/100             1/100   
    Position       Position      Position         Position        Position           Position       Position

Basically, the number is not called digit but it is called a symbol.

The binary number system has 2 different symbols and radix is 2.
The octal number system has 8 different symbols and radix is 8.
The decimal number system has 10 different symbols and radix is 10.
The hexadecimal number system has 16 different symbols and radix is 16.

The following table gives the details of each and what kind of symbols they have

S.No.	Number System	Radix	Digits
1	Binary	2	0,1
2	Octal	8	0,1,2,3,4,5,6,7
3	Decimal	10	0,1,2,3,4,5,6,7,8,9
4	Hexadecimal	16	0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

The hexadecimal number system is used in microprocessors. And the binary is used in advanced and normal computers and by this, there are conversions from binary to decimal, decimal to octal, octal to hexadecimal and other like hexadecimal to decimal, octal to binary, etc.,

And there are binary addition, subtraction, division, and multiplication.

Binary Complement

1's Complement:

The 1's complement of a binary number is the complement of each bit. The complement of 0 is 1 and the complement of 1 is 0. Simply replace 0's by 1's and 1's with 0's.

S.No.	Binary no.	1’s complement
1.	1001	0110
2.	010110	101001
3.	110010	001101
4.	1010 0011	0101 1100

So these are the examples of 1's complement.

2's Complement:

The 2's complement is the binary number that results in adding '1' with the 1's complemented number. See this  it is 

                                              2's complement = 1's complement + 1

Let us see some of the examples

S.No.	Binary no.	1’s complement	2’s complement
1.	1001	0110	0111
2.	010110	101001	101010
3.	110010	001101	001110
4.	1010 0011	0101 1100	0101 1101

These are the Examples for 2's complement.

Have you observed 2nd and 3rd example you think that 1 is added to 2nd position in place of LSB because once check the 1's complement number the last digit is ended up with '1' when we add '1 + 1' we get 10 in binary so 0 remains there and 1 carries so that's why '1' is added in 2nd LSB.

So, Friends, this is about the number system and
...thanks for reading...